Continuous-Time Mean Field Games with Finite State Space and Common Noise

34 Pages Posted: 2 Oct 2019

See all articles by Christoph Belak

Christoph Belak

Technische Universität Berlin (TU Berlin) - Fakultat II - Mathematik und Naturwissenschaften

Daniel Hoffmann

University of Trier

Frank Thomas Seifried

University of Trier

Date Written: September 23, 2019

Abstract

We formulate and analyze a mathematical framework for continuous-time mean field games with finitely many states and common noise. The key insight is that we can circumvent the master equation and reduce the mean field equilibrium to a system of forward-backward systems of (random) ordinary differential equations by conditioning on common noise events. In the absence of common noise, our setup reduces to that of Gomes, Mohr and Souza (2013) and Cecchin and Fischer (2018).

Keywords: mean field games, common noise, Markov chains, regime shifts

JEL Classification: C61, C73

Suggested Citation

Belak, Christoph and Hoffmann, Daniel and Seifried, Frank Thomas, Continuous-Time Mean Field Games with Finite State Space and Common Noise (September 23, 2019). Available at SSRN: https://ssrn.com/abstract=3458336 or http://dx.doi.org/10.2139/ssrn.3458336

Christoph Belak

Technische Universität Berlin (TU Berlin) - Fakultat II - Mathematik und Naturwissenschaften ( email )

Institut fur Mathematik, Sekr. MA 7-1
Strasse des 17. Juni 136
Berlin, 10623
Germany

Daniel Hoffmann (Contact Author)

University of Trier ( email )

15, Universitaetsring
Trier, 54286
Germany

Frank Thomas Seifried

University of Trier ( email )

Department IV - Mathematics
Universitätsring 19
Trier, 54296
Germany

HOME PAGE: http://sites.google.com/site/seifriedfinance/

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